using System; using System.Collections.Generic; using System.Linq; using System.IO; using SB = System.Text.StringBuilder; //using System.Threading.Tasks; //using System.Text.RegularExpressions; //using System.Globalization; //using System.Diagnostics; using static System.Console; using System.Numerics; using static System.Math; using pair = Pair; class Program { static void Main() { SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false }); new Program().solve(); Out.Flush(); } readonly Scanner cin = new Scanner(); readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑ readonly int mod = 1000000007; readonly int dom = 998244353; bool chmax(ref T a, T b) where T : IComparable { if (a.CompareTo(b) < 0) { a = b; return true; } return false; } bool chmin(ref T a, T b) where T : IComparable { if (b.CompareTo(a) < 0) { a = b; return true; } return false; } void solve() { int N = cin.nextint + 1; var A = new ModInt[N]; var B = new ModInt[N]; for (int i = 0; i < N; i++) { A[i] = cin.nextint; } for (int i = 0; i < N; i++) { B[i] = cin.nextint; } var NTT = new NumberTheoreticTransform(); var C = NTT.ConvoluteWithInt32Mod(A, B); ModInt ret = 0; for (int i = 0; i < N; i++) { ret += C[i]; } WriteLine(ret); } } class NumberTheoreticTransform { readonly long mod, primitive_root; public NumberTheoreticTransform() { } public NumberTheoreticTransform(long mod, int primitive_root) { this.mod = mod; this.primitive_root = primitive_root; } public ModInt[] ConvoluteWithInt32Mod(ModInt[] A, ModInt[] B) { long today_mod = ModInt.Mod; long m1 = 167772161, m2 = 469762049, m3 = 1224736769; var NTT_1 = new NumberTheoreticTransform(m1, 3); var NTT_2 = new NumberTheoreticTransform(m2, 3); var NTT_3 = new NumberTheoreticTransform(m3, 3); ModInt[] x = NTT_1.Convolute(A, B); ModInt[] y = NTT_2.Convolute(A, B); ModInt[] z = NTT_3.Convolute(A, B); // garner ModInt.Mod = m2; ModInt m1_inv_m2 = ModInt.Inverse(m1); ModInt.Mod = m3; ModInt m12_inv_m3 = ModInt.Inverse(m1 * m2); ModInt.Mod = today_mod; ModInt m12_mod = m1 * m2; int N = x.Length; ModInt[] ret = new ModInt[N]; for (int i = 0; i < N; i++) { ModInt.Mod = m2; ModInt v1 = (y[i] - x[i]) * m1_inv_m2; ModInt.Mod = m3; ModInt v2 = (z[i] - (x[i] + m1 * v1)) * m12_inv_m3; ModInt.Mod = today_mod; ret[i] = x[i] + m1 * v1 + m12_mod * v2; } return ret; } public ModInt[] Convolute(ModInt[] A, ModInt[] B) { ModInt.Mod = mod; int sz = A.Length + B.Length - 1; int N = 1; while (N < sz) N <<= 1; var G = new ModInt[N]; Array.Copy(A, G, A.Length); var H = new ModInt[N]; Array.Copy(B, H, B.Length); NTT(G); NTT(H); for (int i = 0; i < N; i++) G[i] *= H[i]; NTT(G, -1); Array.Resize(ref G, sz); return G; } void NTT(ModInt[] F, int rev = 1) { int N = F.Length; ModInt h = ModInt.Pow(primitive_root, (mod - 1) / N); if (rev == -1) h = ModInt.Inverse(h); for (int i = 0, j = 1; j < N - 1; j++) { for (int k = N >> 1; k > (i ^= k); k >>= 1) ; if (j < i) swap(ref F[i], ref F[j]); } for (int i = 2; i <= N; i <<= 1) { int m = i >> 1; // zeta = exp(rev * PI / m * i) ModInt zeta = ModInt.Pow(h, N / i); for (int j = 0; j < N; j += i) { ModInt zeta_pow = new ModInt(1); for (int u = j, v = j + m; v < j + i; u++, v++) { ModInt vl = F[u], vr = zeta_pow * F[v]; F[u] = vl + vr; F[v] = vl - vr; zeta_pow = zeta_pow * zeta; } } } if (rev == -1) { ModInt n_inv = ModInt.Inverse(N); for (int i = 0; i < F.Length; i++) { F[i] *= n_inv; } } } // 2^23より大きく,primitive rootに3を持つもの // int[] mods= { 1224736769, 469762049, 167772161, 595591169, 645922817, 897581057, 998244353 }; void swap(ref T a, ref T b) { var t = a; a = b; b = t; } } class FastFourierTransform { public FastFourierTransform() { } public Complex[] Convolute(Complex[] G, Complex[] H) { int sz = G.Length + H.Length - 1; int N = 1; while (N < sz) N <<= 1; Array.Resize(ref G, N); Array.Resize(ref H, N); FFT(G); FFT(H); Complex[] F = new Complex[N]; for (int i = 0; i < N; i++) { F[i] = G[i] * H[i]; } FFT(F, -1); return F; } public long[] Convolute(long[] P, long[] Q) { int sz = P.Length + Q.Length - 1; int N = 1; while (N < sz) N <<= 1; Complex[] G = Array.ConvertAll(P, i => new Complex(i, 0)); Complex[] H = Array.ConvertAll(Q, i => new Complex(i, 0)); Array.Resize(ref G, N); Array.Resize(ref H, N); FFT(G); FFT(H); for (int i = 0; i < N; i++) G[i] *= H[i]; FFT(G, -1); Array.Resize(ref G, sz); return Array.ConvertAll(G, i => (long)Round(i.Real)); } void FFT(Complex[] F, int rev = 1) { for (int i = 0, j = 1; j < F.Length - 1; j++) { for (int k = F.Length >> 1; k > (i ^= k); k >>= 1) ; if (j < i) swap(ref F[i], ref F[j]); } for (int i = 2; i <= F.Length; i <<= 1) { int m = i >> 1; // zeta = exp(rev * PI / m * i) Complex zeta = new Complex(Cos(PI / m), Sin(PI / m) * rev); for (int j = 0; j < F.Length; j += i) { Complex zeta_pow = Complex.One; for (int u = j, v = j + m; v < j + i; u++, v++) { Complex vl = F[u], vr = zeta_pow * F[v]; F[u] = vl + vr; F[v] = vl - vr; zeta_pow = zeta_pow * zeta; } } } if (rev == -1) { for (int i = 0; i < F.Length; i++) { F[i] /= F.Length; } } } void swap(ref T a, ref T b) { var t = a; a = b; b = t; } } /// /// [0,) までの値を取るような数 /// /// camypaper struct ModInt { /// /// 剰余を取る値. /// public static long Mod = (int)1e9 + 7; /// /// 実際の数値. /// public long num; /// /// 値が であるようなインスタンスを構築します. /// /// インスタンスが持つ値 /// パフォーマンスの問題上,コンストラクタ内では剰余を取りません.そのため, ∈ [0,) を満たすような を渡してください.このコンストラクタは O(1) で実行されます. public ModInt(long n) { num = n; } /// /// このインスタンスの数値を文字列に変換します. /// /// [0,) の範囲内の整数を 10 進表記したもの. public override string ToString() { return num.ToString(); } public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; } public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; } public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); } public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); } /// /// 与えられた 2 つの数値からべき剰余を計算します. /// /// べき乗の底 /// べき指数 /// 繰り返し二乗法により O(N log N) で実行されます. public static ModInt Pow(ModInt v, long k) => Pow(v.num, k); /// /// 与えられた 2 つの数値からべき剰余を計算します. /// /// べき乗の底 /// べき指数 /// 繰り返し二乗法により O(N log N) で実行されます. public static ModInt Pow(long v, long k) { long ret = 1; for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod) if ((k & 1) == 1) ret = ret * v % Mod; return new ModInt(ret); } /// /// 与えられた数の逆元を計算します. /// /// 逆元を取る対象となる数 /// 逆元となるような値 /// 法が素数であることを仮定して,フェルマーの小定理に従って逆元を O(log N) で計算します. public static ModInt Inverse(ModInt v) => Pow(v, Mod - 2); } class BinomialCoefficient { public ModInt[] fact, ifact; /// /// 未満でお願いします。 /// /// public BinomialCoefficient(ModInt _n) { int n = (int)_n.num; fact = new ModInt[n + 1]; ifact = new ModInt[n + 1]; fact[0] = 1; for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i; ifact[n] = ModInt.Inverse(fact[n]); for (int i = n - 1; i >= 0; i--) ifact[i] = ifact[i + 1] * (i + 1); ifact[0] = ifact[1]; } public ModInt this[int n, int r] { get { if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0; return fact[n] * ifact[n - r] * ifact[r]; } } public ModInt RepeatedCombination(int n, int k) { if (k == 0) return 1; return this[n + k - 1, k]; } } static class Ex { public static void join(this IEnumerable values, string sep = " ") => WriteLine(string.Join(sep, values)); public static string concat(this IEnumerable values) => string.Concat(values); public static string reverse(this string s) { var t = s.ToCharArray(); Array.Reverse(t); return t.concat(); } public static int lower_bound(this IList arr, T val) where T : IComparable { int low = 0, high = arr.Count; int mid; while (low < high) { mid = ((high - low) >> 1) + low; if (arr[mid].CompareTo(val) < 0) low = mid + 1; else high = mid; } return low; } public static int upper_bound(this IList arr, T val) where T : IComparable { int low = 0, high = arr.Count; int mid; while (low < high) { mid = ((high - low) >> 1) + low; if (arr[mid].CompareTo(val) <= 0) low = mid + 1; else high = mid; } return low; } } class Pair : IComparable> where T : IComparable where U : IComparable { public T f; public U s; public Pair(T f, U s) { this.f = f; this.s = s; } public int CompareTo(Pair a) => f.CompareTo(a.f) != 0 ? f.CompareTo(a.f) : s.CompareTo(a.s); public override string ToString() => $"{f} {s}"; } class Scanner { string[] s; int i; readonly char[] cs = new char[] { ' ' }; public Scanner() { s = new string[0]; i = 0; } public string[] scan => ReadLine().Split(); public int[] scanint => Array.ConvertAll(scan, int.Parse); public long[] scanlong => Array.ConvertAll(scan, long.Parse); public double[] scandouble => Array.ConvertAll(scan, double.Parse); public string next { get { if (i < s.Length) return s[i++]; string st = ReadLine(); while (st == "") st = ReadLine(); s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries); i = 0; return next; } } public int nextint => int.Parse(next); public long nextlong => long.Parse(next); public double nextdouble => double.Parse(next); }